Question 2 a) The following table identifies the probabilities that various numbers of service calls per day will be received by a machine-repair department. Number of calls (x) 4 5 6 7 8 9 P(X) 29 08 29 AZ E 24 06 10 .01 Determine the expected number of calls per day and the variance (3 marks) b) The lifetimes of a certain brand of movie floodlights are normally distributed, with a mean of 210 hours and a standard deviation of 50 hours. Let X be the lifetime of a light picked at random 1. What percentage of the bulbs have a lifetime between 150 and 200 hours? 13 marks) 2. What percentage of the bulbs have a lifetime between 200 and 300 hours? (3 marks) 3. What percentage of the bulbs have a lifetime below 200 hours? 4. What percentage of the bulbs have a lifetime above 300 hours? (3 marks) (3 marks) Total: 15 marks Question 3 a) 1 Find the point estimate and the 95% confidence interval for the mean number of persons riding in a subway car between midnight and 6ama random sample of 40 subway cars had the following number of persons 880 0 2 23 25 29 37 40 41 59 60 60 37 13 15 20 20 20 30 35 35 36 36 36 36 41 41 43 44 47 50 56 61 63 69 70 2232 2 Explain why a 100% confidence interval is useless 71 89 103 (5 marks) (2 marks) b) Describe the steps to performing a hypothesis test Write to the point and add examples to clarify the steps (marks) Total: 15 macks